Systems and methods for recovering implicit physics model under real world constraints

Abstract

Examples including a system described herein implement a novel liquid time constant neural network (LTC-NN) based architecture to recover an underlying model of physical dynamics from real world data. The automatic differentiation property of LTC-NN nodes overcomes problems associated with low sampling rate, the input dependent time constant in the forward pass of the hidden layer of LTC-NN nodes creates a massive search space of implicit physical dynamics, the physics model solver based data reconstruction loss guides the search for the correct set of implicit dynamics, and drop out in dense layer ensures extraction of the sparsest model. Further, to account for perturbation timing error, the LTC-NN based architecture of the system utilizes dense layer nodes to search through input shifts that results in the lowest reconstruction loss.

What is claimed is: 
     
         1 . A system for recovery of model of a dynamical system based on measurement data having a low sampling rate, comprising:
 a processor in communication with a memory, the memory including instructions executable by the processor to:
 access measurement data including a set of traces over time for a dynamical system, the set of traces being sampled at a sampling frequency; 
 apply the measurement data as input to a neural architecture embodied at the processor, the neural architecture having a forward pass configuration that correlates with a bilinear approximation of a set of implicit dynamics of the dynamical system; 
 extract a set of hidden states associated with the measurement data by a plurality of nodes of the neural architecture; and 
 transform, at a dense layer of the neural architecture, the set of hidden states into a set of model coefficient estimates and a set of input shift values that correlate with an over-determined system of equations descriptive of the set of implicit dynamics, the set of model coefficient estimates corresponding with a recovered model of the dynamical system. 
   
     
     
         2 . The system of  claim 1 , the dense layer including a plurality of dense layer nodes whose outputs are used to shift an input vector corresponding with the measurement data that includes a set of user-initiated control inputs (U ex ) applied to the dynamical system over time by a user, the set of user-initiated control inputs (U ex ) having an unknown error and a corresponding set of measured user input activation times having an unknown error. 
     
     
         3 . The system of  claim 1 , the dense layer incorporating dropout to reflect sparsity inherent in the implicit model and the set of measurement data. 
     
     
         4 . The system of  claim 1 , the set of traces including:
 a set of output measurements (Y) of the dynamical system over time including an initial condition value (Y(0)) of the set of output measurements;   a set of system-initiated control inputs (U) applied by the dynamical system over time; and   a set of user-initiated control inputs (U ex ) applied to the dynamical system over time by a user.   
     
     
         5 . The system of  claim 1 , the memory further including instructions executable by the processor to:
 apply the set of model coefficient estimates, the set of input shift values, and one or more instances of the set of traces as input to an ordinary differential equation solver of the neural architecture resulting in a set of estimated output measurements (Y est ); and   evaluate a loss between the set of estimated output measurements (Y est ) and a set of output measurements (Y) of the set of traces.   
     
     
         6 . The system of  claim 5 , the ordinary differential equation solver incorporating a Runge Kutta integration method. 
     
     
         7 . The system of  claim 6 , the memory further including instructions executable by the processor to:
 iteratively update the set of model coefficient estimates to minimize the loss.   
     
     
         8 . The system of  claim 1 , the sampling frequency being less than a generalization boundary that correlates with a sampling frequency threshold where generalization error associated with a model learning method is higher than generalization error associated with a model recovery method. 
     
     
         9 . The system of  claim 6 , the sampling frequency being equal to a Nyquist rate. 
     
     
         10 . The system of  claim 1 , the neural architecture being a liquid time constant neural network architecture.